Sensitive Axis Research Articles

Linear capacitive microdisplacement transduction using phase read-out

This paper describes a principles for capcitive transduction of (micro)- displacements. Transducers based on this principle achieve a fixed, built-in sensitivity which is determined only by the transducer's electrode geometry. This geometry can be manufactured accurately by photolithographic processes. The principle renders the transducer immune to small movements in directions other than the main sensitivity axis and to a small rotation and tilt of the electrode planes. The transducers require only one active electrode plane to which wires must be connected. A realization of the principle in thin-film technology is described. This transducer achieves a resolution better than 25 nm, a measurement span of about 1 cm and a non-linearity smaller than 2 μm peak deviation from linear. A large-scale printed-circuit-board realization with an improved electrode geometry results in even better specifications when the scale factor is taken into account.

Nutation Dampers vs Precession Dampers for Asymmetric Spacecraft

The energy dissipation efficiencies of ball-in-tube dampers oriented with their sensitive axes orthogonal to (nutation) and parallel to (precession) the nominal spin axis of an asymmetric spacecraft are studied using the energy-sink method and numerical integration. Energy-sink equations for each of the two types of dampers are obtained in the forms of damped, periodically forced Hill-type equations. The stability of solutions to Mathieu equation approximations to these equations is considered. An approximate analytical expression for the ratio of the average energy dissipation rates of the two types of dampers is obtained. Results for ideally tuned, identical (except for their spring constants and orientations) dampers are presented and compared with those of a previous study. For a particular spacecraft configuration, analytical results for the energy dissipation ratio are compared with numerical results, and excellent agreement is achieved.

EFFECTS OF CROSS-AXIS SENSITIVITY AND MISALIGNMENT ON THE RESPONSE OF MECHANICAL-OPTICAL ACCELEROGRAPHS

Recorded strong-motion accelerograms may be affected by cross-axis sensitivity and the misalignment of their transducer sensitivity axes. The cross-axis sensitivity arises from the fact that the transducer mass when deflected from its ideal equilibrium position may experience additional deflection caused by the inertial forces perpendicular to the transducer's principal sensitivity axis. The misalignment effects result from imperfect positioning of transducers into the instrument housing so that the nominal sensitivity directions are not mutually perpendicular and/or do not coincide with the orthogonal reference frame attached to the instrument housing. If the misalignment effects cannot be accounted for, the recorded accelerations can be distorted by an amount, which for large input accelerations, may exceed the digitization noise level by as much as one order of magnitude. In this paper a method is presented for a complete dynamic correction procedure which can eliminate any cross-axis and misalignment effects and yield exact accelerations for a reference coordinate system conveniently attached to the instrument housing. To carry out these correction procedures it is necessary to know the precise orientations of all transducers relative to the selected reference frame. A simple sequence of static tilt tests is proposed which provides adequate information for computation of all misalignment angles and estimation of transducer sensitivity constants.

Physiology of peripheral neurons innervating otolith organs of the squirrel monkey. II. Directional selectivity and force-response relations

1. The directional selectivity of peripheral otolith neurons was studied in the barbiturate-anesthetized squirrel monkey (Saimiri sciureus). Each unit's most sensitive axis was characterized by a functional polarization vector. The direction of a centrifugal force was varied with respect to the vector and to the macular plane. The neurons respond in an excitatory manner to shearing forces orthogonally disposed to the vector. The sensitivity to orthogonal shears was usually 10-15% of the sensitivity to parallel shearing forces. There was no significant response to orthogonal compressions, nor did compressions modify the response to shearing forces. 2. Force-response functions were obtained in the stimulus range of +/- 4.92 g. Forces were directed parallel to each unit's polarization vector. The functions are sigmoid shaped and possess both inhibitory and excitatory plateaus. The presumed physiological range of +/-1 g is represented in the lower (concave upward) portion of the function and has a dynamic range, expressed in terms of response magnitude, amounting to 20-40% of the potential dynamic range of the neuron. 3. There was considerable variation among units in their +/- 4.92 g force-response curves. The salient features of the functions are described by three factors, tentatively identified as a transduction gain, a receptor bias, and a mechanical gain. Both the resting discharge (do) and the +/-1 g sensitivity (so) vary in the same direction with changes in the factors related to transduction gain and receptor bias. It is shown that this covariation provides a quantitatively precise explanation for the positive relation between do and so.

Physiology of peripheral neurons innervating otolith organs of the squirrel monkey. I. Response to static tilts and to long-duration centrifugal force.

1. The response to static tilts was studied in peripheral otolith neurons in the barbiturate-anesthetized squirrel monkey (Saimiri sciureus). Each unit was characterized by a functional polarization vector, which defines the axis of greatest sensitivity. A circumstantial criterion was used to assign units to the inferior (IN) or superior (SN) vestibular nerves. The former neurons should innervate the sacculus, the latter mainly the utriculus. Confirming pasting experiments, the polarization vectors for SN units lay near the plane of the utricular macula, those for IN units near the plane of the saccular macula. The polarization vectors for IN units were compared in two groups of animals. In one group, the vestibular nerve was intact; in the other, the superior nerve was sectioned. No differences were found and this, together with other observations, demonstrate that the sacculas in mammals functions mainly (if not solely) as an equilibrium organ. 2. The resting discharge of otolith neurons averages some 60 spikes/s, the sensitivity some 30-40 spikes/s-g. IN units tend to have slightly lower sensitivities than do SN units. IN units with upwardly directed (+Z) vectors have substantially higher resting discharges than do units with downwardly directed (-Z) vectors. The +Z units are also characterized by more linear force-response relations. 3. There is a strong positive relation between the resting discharge and sensitivity of units characterized by regular steady-state discharge patterns. A weaker, but statistically significant, relation is demonstrable for irregular units. It is suggested that the relation seen in regular units is the result of the neurons differing from one anothrer in terms of a receptor bias, a transduction gain, or both. Only the mechanism based on transduction gain is thought to be operative among the population of irregular units. 4. Centrifugal-force trapezoids were used to study the response adaptation to prolonged stimulation. Adaptation was more conspicious in irregular units and was characterized by perstimulus response declines and poststimulus secondary responses. For regular units, adaptive properties were similar during excitatory and inhibitory responses. For irregular units, response declines were larger during excitatory stimuli, secondary responses larger following inhibitory stimuli. Typically, response declines were most rapid at the start of the force plateau. A few units, all of them irregular, exhibited a delayed adaptation with response declines beginning only after a constant force had been maintained for 10-20 s. 5. Excitatory responses of regular units are almost always larger than inhibitory responses. This is so during both the dynamic and static portions of force trapezoids. A similar asymmetry is seen in the dynamic response of irregular units; static response asymmetries of the latter units are more variable.

Test Evaluation of a High Performance Pulse Rebalanced Gyro for Strapdown IMU Applications

Recent mission requirements in the strapdown Inertial Measurement Unit (IMU) field have emphasized the need for inertial sensors which combine the capability of providing precision attitude reference with long mission life. The single-axis hydrodynamic-spin-bearing gyroscope operated with pulse-rebalance servo electronics is a prime candidate sensor for these missions. This paper provides a summary of recent test results and analytical evaluation for a high-performance instrument of this type. The sensor parameters and performance test results summarized in this paper are based on an extensive evaluation program of the 64 PM RIG gas-bearing gyro. The 64 PM RIG design base is the 64 AC RIG (25 IRIG), which was initially developed by MIT, with the primary difference between the two instruments being the use of a permanent magnet DC torquer (rather than an AC torquer) in the 64 PM RIG. The 64 AC RIG was originally developed and produced in large quantities for an inertially-stabilized platform used in a missile application and has since been used as an inertial sensor on several spacecraft programs (OSO-7 and ATS-6). A single-degree-of-freedom gyro, the 64 PM RIG utilizes a hydrodynamic gas bearing, a microsyn pickoff, a magnetic suspension, and a permanent-magnet torquer, and is fully floated to minimize error torques about its sensitive axes. Sensor drift data is summarized which demonstrates the bias variability over a 15 hour period to be less than 0.001 deg/hr. The specific strapdown IMU performance areas which are addressed include sensor scale factor linearity and stability, the noise output of the sensor as characterized by its power spectral density, the attitude reference error buildup as a function of the interval between bias updates, and performance of the sensor in the dynamic environment typically encountered during vehicle maneuvers. The pulse-rebalance technique implemented is binary (forced-limit-cycle), and uses quantized pulse-width modulation of the gyro torquing signal. A dual-scale design of the pulse-rebalanced sensor has been implemented and evaluated. The pulse-rebalanced sensor has a demonstrated capability of maintaining an attitude reference within 1.0 arc-second for time periods exceeding 30 minutes. Test data demonstrating scale factor non-linearity of less than 40 PPM and scale factor stability below a PPM/day is presented. The 64 PM RIG sensor is being incorporated into two strapdown IMUs which will provide the primary attitude reference for the International Ultraviolet Explorer (IUE) and the High Energy Astronomy Observatory (HEAO) spacecrafts. The six-sensor IUE/IMU and the modular two-sensor HEAO/IMU are discussed from the packaging (size, weight, power) and functional viewpoints. Included is a brief description of the hybridized pulse-rebalance servo electronics used for the two programs.

A note on the nonlinear response of the pendulous accelerometer

abstract When the pendulous accelerometer experiences large off-axis acceleration in a direction which produces significant along-the-boom acceleration, the dynamics of the instrument are altered and it becomes nonlinear in its response. The response to an off-axis horizontal acceleration step is derived and found to exhibit small changes in damping, overshoot, damped resonant frequency, and final value of boom position. The size of these effects is negligible for all but the largest accelerations and even then acceptable. The change in overshoot is the largest, about 5 per cent, for an AR-240 strong-motion accelerograph subjected to a 1-g horizontal acceleration step at 45° to the sensitive axis. An expression is developed for the steady-state response to off-axis sinusoidal acceleration. In addition to the proper response, it contains both a double frequency term and a constant offset. The size of these terms is discussed and an example is given.

Directional sensitivity of saccular microphonic potentials in the haddock.

ABSTRACT Microphonic potentials from the sacculus in the haddock have been recorded by implanted electrodes during horizontal vibration of the fish in air. This gives a good simulation of sound stimulation in water. The microphonic potential amplitude was a function of the vibration angle, and from most recording loci maximal amplitudes were obtained for vibration directions parallel to the long axis of the fish. The sensory cells contributing to this response are therefore most sensitive to displacements in the same direction as sound-induced swimbladder pulsations would produce. This result thus supports the theory of an accessory role of the swimbladder in sound reception. Highest sensitivity to vibration directions other than parallel to the long axis of the fish has been obtained from other recording loci. One example of highest sensitivity to a vibration direction at right angle to the long axis of the fish is presented. The findings that different sensory cells appear to have different axes of maximal sensitivity to vibration provides one possible neurological explanation for the ability of fish to detect the direction to a sound source.

Determination of multipole admixtures in quadrupole fields by incremental field measurement by means of a Hall probe

The field strength in an ideal quadrupole field is B( r) = g· r, where g is the gradient and r the distance from the neutral axis. It is possible to check the constancy of the field value at the distance r from the axis by means of a Hall probe, if the probe, which is led on a circle around the neutral axis, follows the given direction of the field also by rotation around its own axis. The two movements are coupled in a program-controlled measuring machine in which an adjusting device aligns the sensitive axis of the probe with its axis of rotation. The respective admixtures of higher multipole orders can be analysed from the fluctuation of the field value along the circle traversed.

大形歯切盤の伝達誤差の測定

A seismic instrument for measuring the hob-to-table cyclic error of large gear hobbing machine is described in which a large and heavy torsional vibration pickup, currently in use for detecting the non-uniformity of rotation of the machine table, is replaced by a pair of small and light rectilinear vibration pickups mounted tangentially on a periphery of the machine table, 180 apart. Two differential-transformer seismic pickups of 1.6 s natural period are connected so as to be additive for the rotational vibration and null each other for the rectilinear vibration of the machine table. The sensitivity for rotational vibration increases in proportion to the table diameter, the minimum measurable angular displacement being 0.0025 sec of arc for the table diameter of 6 m.From theoretical analysis of the motion of the seismic system under working condition, it is shown that the equality of the sensitivities and frequency responses and the parallelism of the sensitive axes of both pickups, and the accuracy of the machine alignment are important factors in determining the measurement error; and these factors are examined in detail. The operating principle of the instrument and the adjustment and calibration of pickups, together with the test results on the bobbing machines of 2 m and 6 m in table diameter, are outlined.

Principles Involved in the LM Rendezvous Radar Redundant Gyro System

For typical failure rates the probability of two or more of four gyros failing is very much less than one or both of two. Thus, a single redundancy system of four gyros greatly enhances system reliability. The orientation of the sensitive axes of four gyros is specified and means of generating outputs dependent only on gyro inconsistencies are defined. The voting logic and plots of switching decision zones are developed. The hardware required to implement this logic is shown to be simple and thus reliable. The use of rate integrating gyros requires the limitation of error integration time in order to avoid spurious failure signals. This is achieved by a reset cycle which realigns the four gyros at regular intervals. False error signals can be generated if inputs are large enough to exceed linear ranges of various components downstream of the gyros.

Calibration studies on a piezoelectric sensing diaphragm for the detection of micrometeorites in space

Laboratory measurements conducted on 100 kHz piezoelectric transducers mounted on a diaphragm similar to the micrometeorite sensors flown on Vanguard III, Explorer VIII, Mariner II and IV are described, which show that the stresses induced at impact are coupled to the piezoelectric sensor predominantly by a bending mode in the diaphragm, rather than by a longitudinal compression radiating from the impact region. Particles impacting at velocities ranging from 10 cm s−1 to 6 km s−1 induce similar vibration modes. The momentum imparted to the diaphragm in this mode, resolved along a normal to the surface, will equal the sum of the momenta of the impacting particle and of the rebounded particle (or ejected matter at hypervelocities), and a piezoelectric crystal mounted with its sensitive axis normal to the surface will develop a signal proportional to the total momentum exchange at impact. Such a system will, therefore, bear resemblance to a ballistic device; the fraction of this momentum which falls within the frequency range of the sensing crystal may, however, be affected by the area of contact and by the contact time of the particle. It is shown that the contact time of small beads can lead to significant errors of calibration.

The response of the horizontal pendulum seismometer to Rayleigh and Love waves, tilt, and free oscillations of the earth

Abstract The horizontal pendulum seismometer is sensitive not only to acceleration along its sensitive axis but also to tilt, variations in the angle of inclination, and along-the-boom acceleration. The complete steady-state response of this type of seismometer to Rayleigh and Love waves, tilt, and free oscillations of the Earth is treated. An equation of motion is developed which includes the effects of tilt, variation in the angle of inclination, and along-the-boom acceleration. An approximate solution to this equation is obtained which separates out the response due to each effect. The response, including these effects, is developed for Rayleigh and Love waves and the conditions under which along-the-boom acceleration and variations in the angle of inclination are important are stated. The question “How much of the seismogram is due to tilt?” is answered in detail for long period Rayleigh waves and free oscillations. It is shown that the seismograms resulting from such waves can require sizable corrections depending on the wave parameters. A correction factor for Rayleigh waves is developed which is universal in the sense that it is independent of the parameters of the particular seismometer and thus applies to all pendulous horizontal seismographs. For Rayleigh waves it is a function only of ellipticity, phase velocity, and period. Correction factor curves for long-period retrograde Rayleigh waves are presented. For circular particle motions a ten per cent correction is required for a three hundred second Rayleigh wave. The problem of obtaining the horizontal ground motion is treated. The response of the horizontal seismometer as a tilt meter is examined; a conversion factor between displacement and tilt magnification is developed. The complete response to simultaneous spheroidal and torsional free oscillations of the Earth is developed. It is shown that the principal response to the low-order spheroidal modes is as a tilt meter. The relationship between the horizontal and vertical seismogram is developed.

3.1 - Traveling-wave laser gyrocompass

A direction-finding device has been designed making use of the properties of the ring laser. The order of magnitude precision for laser gyro is 0.1 degree per hour. The north determination requires long integration time when the plate is static. However, this may be vastly improved by a dynamic method. In this experiment, the ring laser is not rotated about its sensitive axis but about an axis parallel to its plane at constant rate. The beat frequency obtained is frequency modulated. The frequency deviation is proportional to the varying flux of the Earth's rotation through the cavity area. A discriminator detects this modulation. A reference light source which may be displaced about the rotation axis gives a synchropulse every time its beam is normal to the plate. This pulse is fed in a synchronous detector for detection of the output of the discriminator. A feedback control loop sets the reference so that the phase detector gives a null output, that is, when the synchropulse coincides with a maximum of the sine wave. The point source and the rotation axis then define the north direction. Results comparing static and dynamic measurements are given. Accuracy and integration time are discussed.

Transverse sensitivity of piezoelectric accelerometric transducers

The transverse sensitivity of piezoelectric acceleration transducers is caused by the lack of coincidence between the transducer's sensitivity axis and the polarization vector of the piezoelectric plate. This fact should be taken into consideration both in the production of piezoelectric elements, and in the design of transducers and their manufacture.

Pressure-Sensitivity of Accelerometers

The pressure sensitivity of accelerometers has been determined in the frequency range from 20–2000 cps by immersing the transducer in a vibrating column of liquid, as has been suggested by Sykes. If the sensitive axis of the transducer is oriented perpendicular to the axis along which the liquid column vibrates, the transducer will remain at rest, since the pressure gradient along the sensitive axis of the transducer is zero. The pressure sensitivities thus obtained are lower than the acoustic sensitivities obtained in air, using other methods. Various aspects are discussed, such as the frequency dependence of the pressure sensitivity and the pressure sensitivity of cables.

Celestial Rate Sensing

r T 1 H E ANGULAR velocity of a space vehicle can be imJportant to the operations of attitude control and data compensation. Components of angular velocity relative to inertial space resolved along body-fixed axes can be measured by rate gyroscopes fixed in the vehicle with sensitive axes along the prescribed body axes. However, exactly the same components can be determined from the measured velocity of drift of the star field across the fields of view of two or three body-mounted telescopes. This may be called rate sensing/' and may be an attractive alternative to mechanical rate gyros on mechanization grounds. The purpose of this note is to describe the principle of operation of celestial rate sensors of a particular type, and to derive the relationship between the vehicle's angular velocity in inertial space and the output of such an instrument. Mechanization details are not included, largely because these are proprietary features from the viewpoints of the several companies concerned with such developments. For this analysis the telescope and its field are analogous to a pinhole camera and its field. The camera's photographic plate or photocathode (reference surface) and the image of a star produced on it are shown schematically in Fig. 1. A vector directed perpendicularly from the pinhole to the reference surface is denoted by f0. The position of a star image on the plate at time t is given by the vector h. The position of the image, a small time increment At, later is given by f2. The star field is rotating at an angular velocity -co with respect to the camera pinhole and plate, where co is the vehicle's angular velocity in inertial space. The vector velocity of the star image at h is given by (-co X fi). The projection of this velocity onto the plate produces v, the velocity of the star image in the plane of the plate. Note that the projection to the plate is not a perpendicular one but is directed from the pinhole along fx and r2. A base vector reference system eh e2, e3 is presented in the figure; £3 is along fo while ei and e2 lie in the plane of the reference surface. Polar coordinates p and 6 may be used to represent the position of the star image in the plane. The first step is to determine v in terms of p, 6, rQ and co. From the figure it is clear that (f2 — fo)-r0 = 0 and that [f + (-co X fi)Af] X f2 = 0. Expanding the several vectors in the base system and substituting them into these relations, and using the fact that vAt = r2 — h} it can be shown that in the limit as At -> 0

A Statistical Study of the Effects of Electric Fields on the Movements of Mammalian Sperm Cells

A micro technique has been developed to facilitate the study of electric field effects on the swimming pattern of sperm cells. The instrumentation for this technique, a micro-electrophoresis vessel, a metering motion picture projector, and a simple analog computer for data handling, are briefly described. It is shown experimentally that 1) an electric field imposed on a cell suspension acts primarily to direct the cells to the anode without appreciably changing their swimming speed, and 2) the field effects are not linear functions of field strength. It is postulated that the field effect is primarily galvanotaxis and that the cells seek a position of minimum stimulation and therefore must have a transverse sensitivity axis.

An Angular Accelerometer for Guidance

H velocity aircraft and missiles are frequently guided by controlling the angular velocity of the control surfaces. To accomplish this guidance effectively, the primary element of the auto-pilot servo should detect one order higher than angular velocity, that is, angular acceleration. The detection of this angular acceleration is tradionally achieved by employing a rate gyro with a differentiating network in the output of its pick-off. Much simpler is to use an angular accelerometer directly to override the rate gyro, thus eliminating the necessity for a differentiating network; but past experience with conventional angular accelerometers has not been encouraging because of their undesirable sensitivity to linear acceleration and to angular velocity. Both of these handicaps have been overcome in a radically new invention which has been developed at Statham Laboratories. Fig. 1 shows the essentials of a Statham angular accelerometer. The novelty of this angular accelerometer is that its rotor consists of liquid only. When the case is subjected to an angular acceleration, the inertial forces will cause the liquid to rotate and develop a hydrostatic pressure against the paddle as the liquid is forced between the paddle and the baffles. The paddle will deflect angularly until the elastic restraint of the flexure and the pick-off balances the forces on the paddle. This novel construction has been adapted to both unbonded strain gage and inductive pick-offs. The advantages of the Statham liquid rotor angular accelerometer design are apparent after a careful perusal of Fig. 1. Since the liquid mass serves as the rotor, the weight of the paddle which must be supported along the sensitive axis can be made extremely low. In the construction of low range, rigid rotor angular accelerometers, because of the weight of the rotor, ball bearings are frequently employed to contain the rotor spindle. In the liquid rotor design, weak flexures are practical since only a small, rigid mass need be suspended.

Response of the Sperry Rate Gyrotron to Varying Rates of Turn

The response of a tuning fork rate Gyrotron or vibratory gyroscope to steady rates of turn was discussed in a previous paper [J. Acoust. Soc. Am. 26, 56(1955)]. The treatment is now extended to yield the amplitude and phase response of the instrument to impressed oscillation about the sensitive axis. The results can be used in calculating the stability of a servo loop incorporating Gyrotron as an element.